A bus leaves Denver 45 minutes before a second bus.
The first bus travels at 47 mph, and the second bus travels 54 mph.
How long does it take the 2nd bus to catch up to the first bus?
a) Let h= the time the first bus spends traveling. Write the equation you would use to find this time.
__ hours after the first bus left, the second bus catches up. (Round to one decimal place.)
Convert your time from b) to hours to hours and minutes:
___ hours and ___minutes
a) Let h= the time the first bus spends traveling. The equation to find this time is distance = speed x time, or d = st.
The distance the first bus travels is 47h, and the distance the second bus travels is 54(h-45/60) since it leaves 45 minutes later. Setting these equal to each other, we get:
47h = 54(h-45/60)
b) To find the time it takes the second bus to catch up to the first bus, we solve the equation:
47h = 54(h-45/60)
Expanding and simplifying:
47h = 54h - 40.5
-7h = -40.5
h = 5.8
Therefore, it takes approximately 5.8 hours for the second bus to catch up to the first bus.
c) Converting 5.8 hours to hours and minutes:
5.8 hours = 5 hours + (0.8 hours x 60 minutes/hour) = 5 hours + 48 minutes
Therefore, the time it takes the second bus to catch up to the first bus is approximately 5 hours and 48 minutes.
a) To find the time it takes for the first bus to travel, we can use the formula time = distance / speed. The distance covered by both buses at the time the second bus catches up is the same. Therefore, the equation we can use to find the time the first bus spends traveling is:
47 * (h + 0.75) = 54 * h
(Remember, the second bus leaves 45 minutes - which is 0.75 hours - after the first bus.)
b) To find the time it takes for the second bus to catch up, we can solve the equation from step a) for h. This will give us the time in hours:
47h + 35.25 = 54h
35.25 = 7h
h = 5.0357 (rounded to four decimal places)
Therefore, it takes approximately 5.04 hours for the second bus to catch up to the first bus.
c) To convert the time from hours to hours and minutes, we can multiply the decimal part of the time (0.04) by 60 to get the minutes:
0.04 * 60 = 2.4
So, the time is approximately 5 hours and 2 minutes.